Problem: Rewrite as a simplified fraction. ${3.5\overline{41} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}1000x &= 3541.4141...\\ 10x &= 35.4141...\end{aligned}}$ Subtracting the two equations, we have: ${990x = 3506}$ ${x = \dfrac{3506}{990}} $ ${x = \dfrac{1753}{495}} \text{or} {3 \dfrac{268}{495}}$